Optimization approach for the analytical design of an industrial PI controller for the optimal regulatory control of first order processes under operational constraints

Abstract In this paper, an optimization-based approach for the closed-form design of an industrial proportional-integral (PI) controller was proposed for the optimal regulatory control of first order process under three typical operational constraints. An ingenious parameterization with Lagrangian multiplier method was used to convert the constrained optimal control problem in the time domain to an unconstrained optimization problem to derive an analytical solution for the optimal regulatory control. Three typical operational constraints could be taken into account in the controller design stage, explicitly. The proposed analytical design method required no complicated optimization steps and guaranteed global optimal closed-loop performance and stability. The proposed analytical approach also provides useful insights into the optimal controller design and analysis. A practical and facile procedure for designing optimal PI parameters and a feasible constraint set was also proposed.